4.2.22 $y^{\prime }(x)=\sin (x)(2{\sec }^2(x)-y(x))$

ODE
$$y^{\prime }(x)=\sin (x)(2{\sec }^2(x)-y(x))$$ ODE Classification

[_linear]

Book solution method
Riccati ODE, Generalized ODE

Mathematica ✓
cpu = 0.064027 (sec), leaf count = 28

$$\left\{\{y(x)\to c_1{e}^{\cos (x)}+2e^{\cos (x)}\text{Ei}(-\cos (x))+2\sec (x)\}\right\}$$

Maple ✓
cpu = 0.271 (sec), leaf count = 29

$$\{y\left(x\right)=(\int 4\frac{\sin \left(x\right){\mathrm{e}}^{-\cos \left(x\right)}}{\cos \left(2x\right)+1}\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{1}){\mathrm{e}}^{\cos \left(x\right)}\}$$ Mathematica raw input

DSolve[y'[x] == Sin[x]*(2*Sec[x]^2 - y[x]),y[x],x]

Mathematica raw output

{{y[x] -> E^Cos[x]*C[1] + 2*E^Cos[x]*ExpIntegralEi[-Cos[x]] + 2*Sec[x]}}

Maple raw input

dsolve(diff(y(x),x) = sin(x)*(2*sec(x)^2-y(x)), y(x),'implicit')

Maple raw output

y(x) = (Int(4*sin(x)/(cos(2*x)+1)*exp(-cos(x)),x)+_C1)*exp(cos(x))